• Fractal analysis

• Dirichlet forms and their heat kernel estimates

• 2013.08 - 2017.07, B.S. in Mathematics, Tsinghua University, China.

• 2017.08 - 2022.06, Ph.D in Applied Mathematics, Tsinghua University, China.

• 2022.09 - 2025.08, Postdoc, Bielefeld University.

• 2025.10 - Present, Assistant Professor, Center for Applied Mathematics, Tianjin University.

[1] G. Liu and M. Murugan. Parabolic Harnack inequality implies the existence of jump kernel. Potential Analysis, 57: 155--166, 2022.

[2] J. Hu and G. Liu. Upper estimates of heat kernels for non-local Dirichlet forms on doubling spaces. Forum Mathematicum, 34(1): 225--277, 2022.

[3] G. Liu and M. Murugan. On the comparison between jump processes and subordinated diffusions. ALEA Latin American Journal of Probability and Mathematical Statistics, 20: 1271--1281, 2023.

[4] G. Liu. Existence of self-similar Dirichlet forms on post-critically finite fractals in terms of their resistances. Manuscripta Mathematica, 174: 597--647, 2024.

[5] G. Liu. Heat kernel estimates on local and non-local Dirichlet spaces satisfying a weak chain condition. Journal of Mathematical Analysis and Applications, 539: 128477, 2024.